Volume 19: Pages 225-262, 2006
Maxwell's Equations and QED: Which Is Fact and Which Is Fiction?
Randell L. Mills
BlackLight Power, Inc., 493 Old Trenton Road, Cranbury, New Jersey 08512 U.S.A.
The claim that quantum electrodynamics (QED) is the most successful theory in history is critically evaluated. The Dirac equation was postulated in 1926 as a means to remedy the nonrelativistic nature of the Schrödinger equation to provide the missing fourth quantum number. The positive and negative square root terms provided an argument for the existence of negative energy states of the vacuum, virtual particles, and corresponding so‐called QED computer algorithms for calculating unexpected observables such as the Lamb shift and the anomalous magnetic moment of the electron. Dirac's original attempt to solve the bound electron physically with stability with respect to radiation according to Maxwell's equations, with the further constraints that it be relativistically invariant and give rise to electron spin, is achievable using a classical approach. Starting with the same essential physics as Bohr, Schrödinger, and Dirac of e− moving in the Coulombic field of the proton and the wave equation as an equation of motion rather than energy after Schrödinger, advancements in the understanding of the stability of the bound electron to radiation are applied to solve for the exact nature of the electron. Rather than using the postulated Schrödinger boundary condition “Ψ → 0 as r → ∞,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell's equations, the classical wave equation is solved with the constraint that the bound (n = 1)‐state electron cannot radiate energy. Although it is well known that an accelerated point particle radiates, an extended distribution modeled as a superposition of accelerating charges does not have to radiate. A simple invariant physical model arises naturally wherein the predicted results are extremely straightforward and internally consistent, requiring minimal mathematics, as in the case of the most famous equations of Newton, Maxwell, Lorentz, de Broglie, and Planck on which the model is based. No new physics is needed; only the known physical laws based on direct observation are used. Rather than invoking untestable “flights of fancy,” the results of QED, such as the anomalous magnetic moment of the electron, the Lamb shift, the fine structure and hyperfine structure of the hydrogen atom, and the hyperfine structure intervals of positronium and muonium, can be solved exactly from Maxwell's equations to the limit possible based on experimental measurements, which confirms QED's illegitimacy as representative of reality.
Keywords: QED, Maxwell's equations, Lamb shift, fine structure and hyperfine structure of the hydrogen atom, hyperfine structure intervals of positronium and muonium
Received: May 18, 2005; Published online: December 15, 2008